Initial work on multi-family housing, an erratic gauge which plunged 21.3% last month, was a drag on the overall measure. Housing starts for single-family homes rose 3.2% in their third straight monthly increase.

Builders also seem to be looking forward to the next 12 months, requesting the most permits in more than three years.

Permits were at a seasonally adjusted rate of 780,000, a 7.9% increase from April and 25% above last May.

The new data raises the question du jour: Is the housing market making a gradual recovery?

Both the housing starts and building permits measures are at about half the 1.5-million level usually considered healthy. A report Monday found home-builder confidence still weak, despite being at a five-year high.